For ex:- √2
=let us assume that √2 is an rational number.
=let a and b are two co-primes.
√2 is rational so
squaring on both sides
so, 2 divides a² and 2
let, a = 2c
so, 2 divides b² and 2
but according to the fact co-primes do not have the same factor i.e.., a and b have the factor 2
so, this contradicts our fact that √2 is rational.
so that √2is an irrational number